Calculate Velocity of 100 lb Block Dropped onto Stiff Spring

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Homework Help Overview

The problem involves calculating the velocity of a 100 lb block dropped from a height of 5 ft onto a spring with a stiffness of 100 lbs/ft after the spring has deformed 4 inches. The discussion revolves around the concepts of energy conservation and the relationship between gravitational work and spring force work.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the total energy of the mass and spring system, considering both kinetic and potential energy before the drop and at the moment of spring deformation. Questions are raised about the relationship between the work done by gravity and the work done by the spring force.

Discussion Status

The discussion is active, with participants exploring different interpretations of energy conservation and the effects of gravitational and spring forces. Some guidance has been offered regarding the equations to consider, and there is an acknowledgment of the need to clarify the relationship between the forces involved.

Contextual Notes

There is a mention of the spring not necessarily reaching maximum compression at 4 inches, indicating that further motion of the block may occur. Participants are also navigating the constraints of the problem setup and assumptions about energy loss.

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:smile: How do i find the velocity of a block of mass 100 lb being dropped a distance 5 ft onto a spring whose stifness is 100 lbs/ft after the spring has deformed 4 in?

im sure it has somthing to do with work of a spring force but i don't know exactly how. any ideas?
 
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Can you write equations for the total energy of the mass and spring (kinetic and potential) before being dropped and at the moment the spring is deformed 4"? If you can, then you are well on your way to solving the problem.
 
ok ill see what i can do, thanx
 
do i use T1 + U = T2?
 
How does the work done by gravity relate to the work done by the spring force?
 
its in the opposite direction
 
What do they sum to?
 
Dorothy Weglend said:
What do they sum to?
zero.....
 
Well, there you go then. Problem solved.
 
  • #10
No reason to think that the work done by the spring force will equal the work done by gravity. Note that it doesn't say that 4 in is the maximum compression of the spring... the block keeps going!

Instead, consider conservation of energy (assume no energy is lost when the falling block hits the "massless" spring). What's the initial energy of the block just as its being dropped? What's the final energy of the block + spring system when the spring has been depressed 4 in?
 
  • #11
good explanation, i think i got it now thanks 4 help
 

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